Asymptptic Limit Of Euler-Poisson Equations Coupled To A Magnetic Field

The main problem studied in this thesis is the asymptotic limit of the Euler-Poisson equations for the coupled magnetic field.To be more precise,the thesis is mainly focused on the relationship between the incompressible magnetohydrodynamic equation and the Euler-Poisson equations for coupled magnetic fields with debye length approaching zero and low Mach number.The thesis is divided into five chapters.In the first chapter,it is splited into four parts.Firstly,the introduction of model is expounded briefly.Then this thesis mainly elaborates the research meaning of the asymptotic limit of the Euler-Poisson equations coupled to a magnetic field and the current situation domestic and overseas.In the meanwhile,the model is analyzed in asymptotic form and the limit equation is obtained from the form.In the end,the research objectives,difficulties and solutions are given.The second chapter gives the common vector formula,inequality and two important lemmas in the process of proof.The third chapter mainly introduces the main conclusions of this thesis.In the fourth chapter,combined with the special internal structure of the equation itself,the thesis proves that for well-prepared initial data,when the debye length and Mach number tends to zero at the same time,the Euler-Poisson equation coupled to a magnetic field smooth solution converges to the smooth solution of the ideal incompressible magnetohydrodynamic equations by using the classic energy method,the ?-weighted energy estimation method etc.In the last chapter,the result of this thesis is briefly summarized,and the research orientation are put forward based on the current research results.